1. Stating the problem: We want to find the smallest number by which 243 should be multiplied so that the product is a perfect cube. 2. Prime factorize 243: $$243 = 3^5$$ 3. For a perfect cube, the powers of all prime factors must be multiples of 3. 4. Currently, the exponent of 3 is 5, which is not a multiple of 3. 5. Find the smallest exponent to multiply by so that $5 + x$ is a multiple of 3. The next multiple of 3 after 5 is 6. 6. We need to add $x = 6 - 5 = 1$ factor of 3. 7. Hence, the smallest number to multiply is: $$3^1 = 3$$ 8. Final answer: Multiply 243 by 3 to get a perfect cube.